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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
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//
// Author: keir@google.com (Keir Mierle)
// sameeragarwal@google.com (Sameer Agarwal)
//
// End-to-end tests for Ceres using Powell's function.
#include <cmath>
#include <cstdlib>
#include "ceres/autodiff_cost_function.h"
#include "ceres/internal/config.h"
#include "ceres/problem.h"
#include "ceres/solver.h"
#include "ceres/test_util.h"
#include "ceres/types.h"
#include "glog/logging.h"
#include "gtest/gtest.h"
namespace ceres::internal {
// This class implements the SystemTestProblem interface and provides
// access to an implementation of Powell's singular function.
//
// F = 1/2 (f1^2 + f2^2 + f3^2 + f4^2)
//
// f1 = x1 + 10*x2;
// f2 = sqrt(5) * (x3 - x4)
// f3 = (x2 - 2*x3)^2
// f4 = sqrt(10) * (x1 - x4)^2
//
// The starting values are x1 = 3, x2 = -1, x3 = 0, x4 = 1.
// The minimum is 0 at (x1, x2, x3, x4) = 0.
//
// From: Testing Unconstrained Optimization Software by Jorge J. More, Burton S.
// Garbow and Kenneth E. Hillstrom in ACM Transactions on Mathematical Software,
// Vol 7(1), March 1981.
class PowellsFunction {
public:
PowellsFunction() {
x_[0] = 3.0;
x_[1] = -1.0;
x_[2] = 0.0;
x_[3] = 1.0;
problem_.AddResidualBlock(
new AutoDiffCostFunction<F1, 1, 1, 1>(new F1), nullptr, &x_[0], &x_[1]);
problem_.AddResidualBlock(
new AutoDiffCostFunction<F2, 1, 1, 1>(new F2), nullptr, &x_[2], &x_[3]);
problem_.AddResidualBlock(
new AutoDiffCostFunction<F3, 1, 1, 1>(new F3), nullptr, &x_[1], &x_[2]);
problem_.AddResidualBlock(
new AutoDiffCostFunction<F4, 1, 1, 1>(new F4), nullptr, &x_[0], &x_[3]);
// Settings for the reference solution.
options_.linear_solver_type = ceres::DENSE_QR;
options_.max_num_iterations = 10;
options_.num_threads = 1;
}
Problem* mutable_problem() { return &problem_; }
Solver::Options* mutable_solver_options() { return &options_; }
static double kResidualTolerance;
private:
// Templated functions used for automatically differentiated cost
// functions.
class F1 {
public:
template <typename T>
bool operator()(const T* const x1, const T* const x2, T* residual) const {
// f1 = x1 + 10 * x2;
*residual = x1[0] + 10.0 * x2[0];
return true;
}
};
class F2 {
public:
template <typename T>
bool operator()(const T* const x3, const T* const x4, T* residual) const {
// f2 = sqrt(5) (x3 - x4)
*residual = sqrt(5.0) * (x3[0] - x4[0]);
return true;
}
};
class F3 {
public:
template <typename T>
bool operator()(const T* const x2, const T* const x3, T* residual) const {
// f3 = (x2 - 2 x3)^2
residual[0] = (x2[0] - 2.0 * x3[0]) * (x2[0] - 2.0 * x3[0]);
return true;
}
};
class F4 {
public:
template <typename T>
bool operator()(const T* const x1, const T* const x4, T* residual) const {
// f4 = sqrt(10) (x1 - x4)^2
residual[0] = sqrt(10.0) * (x1[0] - x4[0]) * (x1[0] - x4[0]);
return true;
}
};
double x_[4];
Problem problem_;
Solver::Options options_;
};
double PowellsFunction::kResidualTolerance = 1e-8;
using PowellTest = SystemTest<PowellsFunction>;
TEST_F(PowellTest, DenseQR) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = DENSE_QR;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
TEST_F(PowellTest, DenseNormalCholesky) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = DENSE_NORMAL_CHOLESKY;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
TEST_F(PowellTest, DenseSchur) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = DENSE_SCHUR;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
TEST_F(PowellTest, IterativeSchurWithJacobi) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = ITERATIVE_SCHUR;
options->sparse_linear_algebra_library_type = NO_SPARSE;
options->preconditioner_type = JACOBI;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#ifndef CERES_NO_SUITESPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingSuiteSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = SUITE_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_NO_SUITESPARSE
#ifndef CERES_NO_ACCELERATE_SPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingAccelerateSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = ACCELERATE_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_NO_ACCELERATE_SPARSE
#ifdef CERES_USE_EIGEN_SPARSE
TEST_F(PowellTest, SparseNormalCholeskyUsingEigenSparse) {
PowellsFunction powells_function;
Solver::Options* options = powells_function.mutable_solver_options();
options->linear_solver_type = SPARSE_NORMAL_CHOLESKY;
options->sparse_linear_algebra_library_type = EIGEN_SPARSE;
RunSolverForConfigAndExpectResidualsMatch(*options,
powells_function.mutable_problem());
}
#endif // CERES_USE_EIGEN_SPARSE
} // namespace ceres::internal